Cory is reluctant to leave her home and attend college despite just being finished with her teenage years. Usually, the people of this age are explorative and are trying to find their identity in the world separately, but Cory seems to stay isolated even from Mike, which indicates that she might be going through the stage of stress. Stress makes a person to avoid any kind of interaction with other people and inhibits the urge to explore the life outside one's comfort zone. So, Cory is going through the stress stage.
I believe the experiment was too see if the flowers that would grow from the stem would turn out to be red in color. (Which is the reason they put red ink.)
